70 DLSIAFECTANT.S 



This can be shown graphically by plotting the loga- 

 rithms of the death times against the logarithms of the 

 concentration. This type of plotting must result in a 

 straight line, as the following reasoning indicates. In the 

 determination of death times, the right side of the 

 equation 



initial number 

 Ktc" = log - 



survivors 



is not affected by changes in concentration because all 

 tests of a series begin with the same initial number and 

 end with the same number of survivors, theoretically 

 very few, practically none. K, the deathrate constant 

 for c = i, is also constant. We therefore obtain 



tC^ = M 



where M is a constant. Dividing the two members by t 

 and taking their logarithms, we have 



n log c = log M - log t 



where log M is a constant. Therefore log t is a recti- 

 linear function of log c, and n controls the slope of the 

 line. Figure 16 shows the different slopes produced by 

 different values of n. Figure 17 shows the curves for 

 phenol and formaldehyde crossing each other. Curves 

 for other disinfectants may be found in Figure 22. 



The meaning of the concentration exponent in the le- 

 thal reaction of bacteria is not clear. In chemical reac- 

 tions, it frequently indicates the number of reacting 

 molecules. In the case of disinfection, this seemed rather 

 improbable to Watson (1908) because n is not always an 

 integer. Further, the not uncommon value n = 0.5 

 should indicate that two molecules of bacterial protein 

 react with one molecule of disinfectant, which seems 

 highly improbable for such disinfectants as HCl or 0:-. 

 But the assumption that n corresponds to a given num- 



